When describing SEM to others, I've been asked more than once whether some Bonferroni-type correction is included when using the alternative models strategy. How do you answer the "data mining" question? Any references or polite phrasing would be appreciated. Thanks!

When this comes up to me, I just acknowledge the fact that yes this is an issue in SEM just as it is an issue in all statistical testing. And the solution is to be conservative in assessing significance just as Bonferroni does. Benferroni however, is probably unnecessarily conservative given that the multiple tests are not independent. I'm not aware of any studies on this topic or any useful references. Perhaps a dissertation is in order.